English

On squares, outside guessing of clubs and I_{<f}[lambda]

Logic 2016-09-06 v1

Abstract

Suppose that lambda = mu^+. We consider two aspects of the square property on subsets of lambda. First, we have results which show e.g. that for aleph_0 <= kappa =cf (kappa)< mu, the equality cf([mu]^{<= kappa}, subseteq)= mu is a sufficient condition for the set of elements of lambda whose cofinality is bounded by kappa, to be split into the union of mu sets with squares. Secondly, we introduce a certain weak version of the square property and prove that if mu is a strong limit, then this weak square property holds on lambda without any additional assumptions

Keywords

Cite

@article{arxiv.math/9510216,
  title  = {On squares, outside guessing of clubs and I_{<f}[lambda]},
  author = {Mirna Džamonja and Saharon Shelah},
  journal= {arXiv preprint arXiv:math/9510216},
  year   = {2016}
}